by Filip Palda
This is not to say that people cannot differ in their desired tradeoffs, but rather that such differences may be less frequent than we imagine. Preference functions with different absolute levels of joy that produce similar desired rates of tradeoff when consuming goods in similar proportions are said to possess “homothetic” indifference curves. Even if their conception of the individual may be questioned by other social sciences, economists are certainly gifted creators of funky sounding jargon.
Gold in the theory
THE RELATIVE REASONING behind utility maximization has a practical side. Businesses do not need a window into the souls of consumers to see how much pleasure they get from different products. Businesses simply need a reflection. Some idea of the ratio of pleasures and how easily that ratio can be made to change as consumption patterns change are all you need. This means figuring out whether shifting relative prices a little will bring you lots of consumers, which economists call somewhat bizarrely “the elasticity of substitution”. This elasticity came to the fore in the early 2000s when a few companies realized that most people would gladly give up sound quality in their music for ease of use. In economic jargon, they perceived that the indifference curve between sound quality and ease of use was quite flat. In more normal terms, a few businesses figured out that people could easily be convinced to give up one feature for another. This realization gave rise to the iPod and its imitators, which used new technology to pack the equivalent of a thousand cassette tapes into a music player the size of a credit card.
People gladly emancipated themselves from incarceration in sacrosanct hi-fidelity basement dens lined with hundreds of reel-to-reel tapes and CDs in exchange for the freedom to roam wherever they pleased, even if it meant listening to tunes through ear-stretching plastic plugs. The insight behind this revolution in consumption lay in recognizing that people could be easily coaxed by a change in prices to trade off sound quality for the heightened convenience of portable access to a vast library of tunes, and to accelerate this shift with new technologies that brought down the price of convenience relative to quality. Businesses did not need to know anything about how much absolute pleasure consumers were getting. All they needed to clue into was relative pleasure.
Substitution as the road to riches
SUBSTITUTION IS NOT only the basis of the theoretical analysis of how people spend their money, but also a practical guide to what needs to be done to create riches. The rule for maximizing utility, or getting the most happiness, was that you had to consume a product up to the point where what you had to give up for another product was equal to what you were willing to give up. The exercise was predicated on being able to measure consumption in fine portions the way a coffee bean dispenser at the supermarket does.
Happiness would be difficult to attain if you could only buy coffee in the 37,500 pound blocks traded on the New York Intercontinental Exchange. Your choices would be stark. Either mortgage your house and turn your garage into a warehouse, or drink no coffee. With the exception of food, clothing, perfume, and medications, many of the goods we buy are of the all-or-nothing sort. One can only buy a whole car, not a part of one, or a whole house, or a whole refrigerator. The indivisible nature of these big consumer items makes it a challenge for a person to finesse his or her consumption to the point where preferences are in line with possibilities and often leave him or her with poorly satisfied demand.
The challenge and opportunities that indivisibilities pose for creating riches goes back to the time of primitive humans. Slaughtering a woolly mammoth required Cro-Magnon tribes to hold giant barbecues on the spot. They had no storage technology, other than perhaps smoke-curing, which would allow them to space consumption over a few weeks of meat shortages. They certainly had no freezers. Cro-Magnon man was a rough-hewn sample of humanity, living at the limits of his physical capacities, who had to be strong in order to cope with the ups and downs of the food supply. This hearty specimen faded from history once people discovered how to tend sheep and other flocks of small animals that could be moved from pasture to valley according to the season. Animal husbandry was in essence a storage “technology” for spacing consumption evenly across the seasons. A flock of sheep equal in mass to a mammoth could be consumed at leisure in manageable quantities and did not call for the skills and power of a rodeo rider coupled with the courage of a beast master.
By substituting consumption today for consumption tomorrow, humans may at this stage not have grown rich, but they certainly enhanced their chances of survival. Taming beasts and breeding them down to handy sizes did not only allow our ancestors to substitute consumption across time and in manageable packets. It also facilitated substitution across space. This is called spot trade: I give you something now in return for you giving me something now. Trade is beneficial to all because even though nature endows all of us with different abilities and sources of wealth, rarely do these endowments conform to our desires. Early farmers were good at growing barley, but found that a diet of grains was more palatable with meats. They traded their surplus grain for tasty lamb chops with mountain peoples who lived in an environment suitable to animal husbandry. The “parcelization” of food helped in this trade.
Hand-in-hand with advances in parcelization came advances in measurement. For finely graded exchanges to take place you needed a precise idea of how much mutton you were giving away in exchange for how much barley. From this need to trade was born metrology, the study of weights and measures; likely the oldest science. Without metrology, trade would have remained limited by fears of receiving too little or giving away too much. Metrology allowed people who did not know each other to “trust but verify” and gave the incentive to Egyptians, Mesopotamians, and Chinese to discover and develop complex techniques of mass cultivation. Governments from these eras carved in stone and pressed into clay the punishments for those who tampered with balances and weights. Many of the measurement standards from five thousand years ago remain with us, including the inch and the grain. Governments paid close attention to weights because healthy markets that produced private wealth were the source of government wealth through taxation.
Today, attempts to enhance substitutability continue to follow the same path in search of physical divisibility and enhanced measurement. We push technology forward to allow a finer physical division of products so that we may exchange them in ever closer conformity with our needs.
The market for gems exploded in the 1980s when technology advanced to allow miniscule diamonds to be cut. No longer did you have to trade off your motor-home for a three carat diamond ring. Now quarter carat diamonds could be cut in solitaire or emerald styles at costs that required nothing more than the sacrifice of your scooter. Of course, smaller diamonds are not as desirable as larger ones, but their appearance on the retail market relieved people of average wealth from the difficult bulk trade-offs they had been forced to make in an earlier period when technology restricted cut diamonds to being big and expensive. Enhanced techniques of measuring and certifying the carat content and clarity of the product gave buyers the confidence needed to plunk down their hard earned dollars.
The story of the revival of the diamond industry illustrates why substitution is perhaps the most important concept in economics. Most of what people consume is not really new products, but old products made available in more convenient and reliable formats. Today we think nothing of buying one less cup of coffee so that we can purchase a single tune or other type of sound recording through an online retailer. Yet, up until the late 1990s, to own a single song you liked you had to buy an entire album of tunes, most of which you did not fancy. The album would cost you more than a cup of coffee and the bulk nature of the purchase left you frustrated. As digital technology and the savvy to market it matured the sale of individual tunes through the internet and their storage on USB devices became possible and affordable. The results were enormous profits for internet digital music retailers and unprecedented convenience for consumers.
> These ubiquitous benefits had to do with creating new products, and they also had to do with making an old product available in a more divisible, that is, substitutable format than before. The increased substitutability that resulted allowed consumers to bring into closer line their willingness to exchange goods with their ability to exchange them.
The example of the digitization of songs shows how transforming the physical nature of a product by reducing it to smaller parts can enhance our ability to substitute one good for another in closer conformity to our needs. But breaking down consumables into smaller physical parts has limits, and in certain cases makes no sense at all. You cannot break a car down into something smaller without destroying its function. You cannot cut a song in two and sell the first half as a meaningful expression of the artist’s idea. What you can do is think about what a car does for the consumer.
Renting substitution
UNLIKE A SLICE of salami, you do not “consume” a car at one sitting. Instead, you enjoy a stream of services from the car over its driveable life. While the physical entity we call a car may not be divisible into smaller parts, this stream of services is divisible and can be sold in packets of as small as several hours. This is called rental.
Rental is the sale of a durable object’s services for a period agreed upon by the owner and the buyer. By renting a house for a month or a year, you escape the constraint of having to make an all-or-nothing decision about its purchase. Imagine the paralysis in airport travel if to fly one had to buy the plane. What would happen to the tourist industry if instead of being able to rent a car, the out-of-towner had to buy it?
The benefits of parcelling out streams of services from durable objects is so huge that the search for new ways of renting old products is a path to riches for the innovator clever enough to discover a new rental “technology”. It may seem like a strange way of using the word, but technology is what is at play in the evolution of the rental market.
Of course, some form of rental has been possible since at least Roman times when five storey insulae housed the urban proletariat. Rental was simple because apartment buildings were always fixed to the ground. In contrast, renting horses or clothes or furniture was always problematic because these were not fixed and could be stolen. Today you can rent just about anything that moves. What makes this possible are multi-billion dollar tracking systems, armies of repossession agents, legal institutions, and computer encryption techniques that allow an electronic book to be borrowed for two weeks and then removed from your computer. In all these cases the technology enables the enforcement of the contract to return the rented object to its owner. This is a very different technology from the one used to split a product into smaller physical parts for sale, but it is of similar importance in multiplying the consumer’s opportunities for substitution.
Peering into the deeper meaning of rental helps us appreciate that consumers like it when they are offered the opportunity to substitute a little bit more of one product for a little bit less of another. Substitution allows them to arrange the variety of things they consume until the marginal relative worth they place on any two items is the same as their relative cost in the market. These are important manifestations of substitution, but we have not really taken the thought to its limit. Thus far, our line of reasoning has assumed that consumers take prices as given. They then adjust their consumption in line with these prices. Imagine what would happen if consumers could adjust prices.
Prices are in your hands
ADJUSTING PRICES TO our wishes seems like a daydream until we realize that what we buy is not always what we consume. No one eats a frozen turkey just bought from the supermarket. You need to defrost the turkey, perhaps in the microwave. Then you need to season it, stuff it, and cook it, possibly in a computerized convection oven. Seen in this light, the frozen turkey is just one of several “inputs” into a production process that requires your time and the use of fairly sophisticated modern kitchen equipment. The “output” is a processed food product that generates satisfaction. The cost of all the inputs needed to produce one plate of cooked turkey is the real price the consumer faces.
This is where a consumer’s empowerment begins. There is nothing that the consumer can do to change the supermarket price of the frozen turkey. But he or she could invest in an appliance that cooks efficiently and delivers a tender, tasty product. Instead of tending to the turkey herself, a busy executive could instead enlist the help of her children on the weekend to baste the beast while she pores over excess work from her office. This substitution of the executive’s time for the children’s time also lowers the cost of obtaining the final product.
The home is a factory in which the allocation of labor and the use of productivity-enhancing technology such as ovens, power tools, cleaning equipment, garden tractors, and pesticides allow a family to lower the cost of consuming a final product. This is why families that live on farms may have little money, but are sometimes well-off. The household production technology of farmers may be sophisticated enough to allow them to be cash poor, but product wealthy.
A family should invest in household technology according to a calculation. It should consider how much of other goods they must give up to buy the technology compared with the extra product it receives at home from the enhanced productivity flowing from the technology. It is a complicated equation that need not concern us here. What matters for our purposes is to understand that improvements in domestic production technologies give people more scope to decide how best to shuffle their resources.
From consumers to capitalists
SO FAR WE have only looked at how consumers can best arrange their expenses. That logic leads to an understanding of the demand curve. The logic shows how people react to prices. The bonus from learning about substitution in the context of what economists call “consumer theory” is that you also get producer theory. With producer theory comes an understanding of the supply curve. This is why some higher-level economics courses prefer to start with consumer theory. Once it is mastered, producer theory can be instantly accessed.
The link between the way firms and consumers behave can be understood by noting that the solution to arranging purchases so as to maximize utility given a certain income and facing certain prices, can be arrived at by the logic of cost minimization. As we saw in the discussion of the Slutsky equation, maximizing utility and minimizing the cost of attaining any given level of utility are inseparable companions. Businesses face similar problems to those of the consumer. In fact, businesses are remarkably similar to consumers. They have an objective: to maximize profits. And they have a constraint, but one which is a bit different from that of consumers. Consumers have a fixed budget which they must divide between goods of fixed price.
Businesses have no fixed budget constraint. They want to sell as much as they can, and will spend any amount on workers and machines if the demand is there. The constraint on businesses is one of technology. A business wants to combine its workers and machines in such a way as to minimize the cost of producing any given level of output. But what do machines and workers combine into? Economists call it a production function. It summarizes the relationship between inputs of workers and machines and outputs of goods. That is what economists mean when they speak of technology. It is a constraint on the business because it limits how much it can produce given a certain quantity of raw inputs.
What do businesses do with this production function? Just as the consumer sought to minimize the cost of attaining any level of utility, the business seeks to minimize the cost of producing any given level of output. The rule for doing so is identical to that used by the consumer. The business must combine workers and machines in such a way that the output produced by an extra unit of labor relative to that produced by an extra unit of machines is equal to the ratio of wages to the cost of machines. If at a given level of production an extra unit of labor contributed twice the output as an extra machine but cost three times as much, then the same le
vel of output could be produced at lower cost by reducing labor and increasing machines. So the business must adjust its mix of inputs until it is indifferent as to whether it increases output by using more of one and less of another.
Such is the logic of cost minimization. From this logic we can discover how businesses will change their use of inputs as their prices change. More interestingly, the logic of cost minimization reveals the business’ cost function to be the basis of its supply function. A business’ cost function arises from its attempts to arrange inputs in such as way as to minimize the cost of producing a certain level of output. In this sense it should really be called a minimum cost function, as it shows the minimum cost of producing any given level of output. You can also use the cost function indirectly to calculate the minimum cost at which the business could increase output by one unit. This is called the marginal cost at a given level of output. If you do this calculation for each subsequent increase in output you can string together the marginal cost function. If marginal cost increases as you produce more this means that it is becoming harder to combine inputs in as efficient a way as when you produce less.
Economists call increasing marginal cost “diminishing returns” and believe it characterizes almost all production processes. While the logic of cost minimization guides the firm in combining inputs efficiently for any given level of output, the logic of profit maximization goes a step further. Firms use their marginal cost function to determine what their level of output should be given the market price for the product. If a product sells for $5 a unit and it costs only $3 to produce an extra unit (marginal cost) then you are producing too little. You can increase your profits by increasing output to the point where diminished returns raise your marginal cost to the level of the price. Using this reasoning, if price increases then once again your marginal costs are below price and you should increase output. It is in this sense that the marginal cost curve shows how a business will change output in reaction to price. Economists call this reaction function a supply curve. It is an amalgam of the price of labor and machines, and the “parameters” or basic elements of your production function.